Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-2y &= -7 \\ 7x+2y &= -7\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = -7x-7$ Divide both sides by $2$ to isolate $y$ $y = {-\dfrac{7}{2}x - \dfrac{7}{2}}$ Substitute this expression for $y$ in the first equation. $-x-2({-\dfrac{7}{2}x - \dfrac{7}{2}}) = -7$ $-x + 7x + 7 = -7$ Simplify by combining terms, then solve for $x$ $6x + 7 = -7$ $6x = -14$ $x = -\dfrac{7}{3}$ Substitute $-\dfrac{7}{3}$ for $x$ back into the top equation. $+ \dfrac{7}{3}-2y = -7$ $\dfrac{7}{3}-2y = -7$ $-2y = -\dfrac{28}{3}$ $y = \dfrac{14}{3}$ The solution is $\enspace x = -\dfrac{7}{3}, \enspace y = \dfrac{14}{3}$.